approved for public release; distribution unlimited. · form approved report documentation"...
TRANSCRIPT
P.L-TN--92-1016 -, AD-A260 016 PL-TN--~lI~iII~III$111 1It I 92-1016
A FIGURE OF MERIT FOR TRANSIT-TIME-LIMITEDTIME-DERIVATIVE ELECTROMAGNETIC FIELDSENSORS
Carl E. Baum
January 1993
APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED.
KL~UC'TJp&426lS '93-01344 1111111111111111l11111 n l fl II
PHILLIPS LABORATORYAdvanced Weapons & Survivability DirectorateAIR FORCE MATERIEL COMMANDKIRTLAND AIR FORCE BASE, NM 87117-6008
DISCLAIMEI' NOTICE
THIS DOCUMENT IS BEST
QUALITY AVAILABLE. THE COPY
FURNISHED TO DTIC CONTAINED
A SIGNIFICANT NUMBER OF
PAGES WHICH DO NOT
REPRODUCE LEGIBLY.
Form Approved
REPORT DOCUMENTATION" PAGE OMB No. 0704-0188
P Ic r o.( Ourden *or thr ' 11i tlorn ttn tor ration s ost)tl d to averaqe i ,our per espooe. iniuducng the time for r"vewngq instrutilon•. searching existing data sources,gatherinq and maintaininq the data ned•od, and comnpleting inO -v -r'q the .olledlion of information Send comments rogarding this burden estimate or any other aMwect of this,oDleton of informnation. *no ud nq SupJpct r• for rcun.q this birded to Washington Hea~duartefs Servites. Directoratn of information Operations and Reports. 1215 JeffersonDavis Highway. Suite 1204 Alhnr1ton.4JA 22202-4301 .and to the Office ot Management and Budget. Paperwork Reduction Project (0704-0188). Washington. DC 2)503.
1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVEREDJanuary 1993 Technical Note
4. TITLE AND SUBTITLE S. FUNDING NUMBERS
A FIGURE OF MERIT FOR TRANSIT-TIME-LIMITEDTIME-DERIVATIVE ELECTROMAGNETIC FIELD SENSORS
6. AUTHOR(S) PR: 9993TA: LA
Carl E. Baum WU: BS
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATIONREPORT NUMBER
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORINGAGENCY REPORT NUMBER
Phillips Laboratory PL-TN- -92-1016Kirtland AFB, NM 87117-6008
11 SUPPLEMENTARY NOTE SSensor and Simulation Notes, Note 212, 8 December 1975.
Publication of this report does not constitute approval or disapproval of the ideas
or findings. It is published in the interest of scientific and technical*
12a. DISTRIBUTION / AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE
Approved for public release; distribution unlimited.
13. ABSTRACT (Maximum 200 words)
This note derives a sensitivity-bandwidth figure of merit for comparing theperformance of sensors designed to measure the time derivative of D or B. Thisfigure of merit is a dimensionless number combining sensitivity and upper frequencyresponse (bandwidth) in a form equivalent area times the square of bandwidth. Thelarger the figure of merit A, the more efficient is the design. This figure ofmerit is appropriate where sensor size is not a factor, but sensitivity and
bandwidth are of primary concern.
*information exchange. The established procedures for editing reports were not
followed for this Technical Note.
14. SUBJECT TERMS 15. NýMBER OF PAGES
Sensitivity-Bandwidth, Figure of Merit, Electromagnetic Fields, 16.PRICECODE
Time Derivative
17. SECURITY CLASSIFICATION 18 SECURITY CLASSIFICATION J19, SECURITY CLASSIFICATION 20 LIMITATION OF ABSTRACTOF REPORT OF THIS PAGE OF ABSTRACT
1 Unclassified Unclassified Unclassified I SAR""_• ._ " Al_ _ __o____0 5__'____/
Sensor and Simulation NotesNote 212
8 December 1975
A Figure of Merit for Transit-Time-LimitedTime-Derivative Electromagnetic Field Sensors
Carl E. BaumAir Force Weapons Laboratory
Abstract
This note derives a sensitivity-bandwidth figure of merit for com-paring the performance of sensors designed to measure the time derivativeof D or B. This figure of merit is a dimensionless number combiningsensitivity and upper frequency response (bandwidth) in a form equivalentarea times the square of bandwidth. The larger the figure of merit A,the more efficient is the design. This figure of merit is appropriate wheresensor size is not a factor, but sensitivity and bandwidth are of primaryconcern.
D U Y INSPEC'LTD I
ITIS QMalDTIO TAB 0
Justltiostio
By
AvailabilIty CodesAvail and/or
Nset Speoial
I. Introduction
In designing sensors for the time derivative of electromagnetic fields
one would like to have quantitative parameters for deciding what are the2.5best designs. Previous notes have discussed the concept of equivalent
volume Veq and a figure of merit based on the ratio Veq/V where Vg is
an appropriate geometric volume ,.n which the sensor is to be enclosed.
Such a figure of merit is a measure of how efficiently the sensor fills the
specified geometrical volume. Based on the usual electromagnetic scaling
procedures this dimensionless figure of merit is independent of size for a
given sensor design shape. This figure of merit is appropriate where
enclosing volume is a constraint on the sensor design. For defining this
equivalent-volume figure of merit the sensor was assumed electrically
small for all frequencies of interest and the characteristic LI R time for
loops and RC time for electric dipoles was assumed large compared to
transit times on the sensor geometry.
This note defines a different figure of merit based on a different
type of design constraint. Let us asst me that the sensor can be any size
or shape for measuring electromagnetic fields in an incident plane wave
propagating in the 11 direction with unit vectors 12 and 13 for polarizations
as illustrated in figure 1. 1 and with orthogonality conditions
11x1 2 3A 1 2 1 3 =~ 1 3 x 1=1 2-0 (1. 1)
1 1 = 6 , n,m=1,2, 3 (orthogonal unit vectors)n m n, m
Let the surrounding medium be free space with permittivity c and per-0
meability uo for which we have
1 5Z = sc (1.2)
0 c
E
12
-I/-
sensor volume V.bounded by surface S.
Figure I.I. Electromagnetic Field Sensor in Free SpaceIlluminated by a Uniform Plane Wave
2
where s is the Laplace transform variable (two sided) corresponding to
time dependence est for CW purposes. Our incident plane wave is then
described by
r rt)(
E~rt 0 Eff 2 t - 1 1.-
H. i(r,t) = 11 X E. (rt)Hinc Z 1 inc
00-t 1 r• / f1er•
-o jf 2 (t - f 3 (t (1.3)
E -ZH0 00
or in Laplace form by
E (r, s)= E f(s) 1 + f(s) 1 e_ n 1 2 -23 3 1 " (1.4 )
incrW , Hss)1 3 3 oi e
where the tilde -over a quantity indicates th,3 Laplace transform as
00 1-0 +iaoS() = f(t) -St dt f(t) 1= J f(s)e ds
(1.5)
s = + ito
with 0 to the right of any singularities in the complex s plane. For pre-
sent purposes constrain the incident wave to have a single polarization
1e for electric field and 1h for magnetic field as
,4
e h ~ e h
E. (r'.s) =E f(s) einc o e (1.6)
-. ~-y -* r.1
H. (r,s) = H f(s)e Ihinc oh
In this note we first review the characterization of the sensor
response under the assumption that the sensor is electrically small. Then
we introduce the high frequency limitation as the characteristic frequency
or time for which the ideal time derivative behavior becomes invalid.
Considering the power delivered to the load at this maximum frequency
appropriately normalized to the power in the incident wave and accounting
for the time derivative nature of the response an appropriate dimension-
lest figure of merit is defined.
The sensors of concern are designed to measure a broadband tran-
sient pulse and often drive a coaxial or twinaxial transmission line of
characteristic impedance Z which is approximately frequency indepen-c
dent. We then assume that the load is purely resistive and frequency
ind,:pendent and denote its value by Z . In common practice Z is 50 ohmsc c
(co.ax for single ended outputs) or 100 ohms (twinax or two coax in series
for differential output), although other constant resistive impedances are
possible.
II. Electrically Small Antennas
By electrically small antennas (or scatterers) is meant that the
maximum linear dimension is small compared to the radian wavelength
X (or yi1-1 in the complex frequency sense). More strictly it means that
the first terms in the low frequency expansion (around s = 0) are adequate
to describe the open circuit voltage and short circuit current from the
antenna. For electric and magnetic dipole sensors these have well-known
forms.
A. Electric dipole sensors
An electric dipole is constructed by two separated conductors 7
(perhaps containing some impedance loading). This can transmit an elec-
tric dipole field at large distances and low frequencies by its electric
dipole moment. As a sensor (receiving antenna) its induced electric
dipole moment is of concern and leads to a concept of an equivalent length
(height) and an equivalent area both of which are constant vectors. In
free space its impedance at low frequencies is described by a capacitance,
This leads to equivalent circuits as in figure 2. 1.
Such a sensor has basic parameters at low frequencies
C sensor capacitance
I- e equivalent length (height)e eq
A equivalent areaeeq
which are related by
e E eeq o eq
A C I•eeq o eq (2.1i)
A AIIeeq e eeq eeq
0+
C
- *E. Ve- q Inc -
sensor flood
A. Thevenin equivalent circuit
2"0q at Inc
0
sensor I load
B. Norton equivalent circuit
E inc+
VOC°. !T o.c.
C. Electric dipole sensor
Figure 2.1. Electrically Small Electric Dipole Sensor in Free SpaceI _
We also have (with fields evaluated at the sensor "location" r = 0)
V -. E. open circuit voltageo.c. e inceq
s o A a D. short circuit currents.c. e 8t mneeq
D. = EE.Lnc o inc
sCZVo. c. 1 + sCZ voltage into load
c (2.2)
S.C. 1 + sCZ current into loadC
Z 1 source impedance
I Be co
V z load impedanceC
IE
e Ceq C eeq e eq eeq eeq eeq
equivalent volume
B. Magnetic dipole sensors (loops)
A magnetic dipole is constructed by a conducting loop7 (perhaps
with some parallel impedance loading). This can give a magnetic dipole
field at large distances and low frequencies by its magnetic dipole moment.
As a sensor its induced magnetic dipole moment leads to the concepts of
vector equivalent length and equivalent area. The low frequency imped-9o
ance is an inductance. Equivalent circuits are given in Figure 2.2.
This type of sensor has basic low-frequency parameters
8
=/
A . +V zheq inc Lc
I
sensorI loodI
A. Thevenin equivalent circuit
®o
H~q L V
sensor (load
B. NErton Squivalent circuit
H 'inc
C. Magnetic dipole sensor (loop)
Figure 2.2. Electricolly Small Magnetic Dipole Sensor in Free Space
CI
L sensor inductance
I h equivalent lengtheq
Aeh equivalent areaeq
which are related by
h P~ heq o eq
h h (2.3)eq o eq
~heq E jLe Ieq - eheq I eq(
We also have (with fields evaluated at the sensor "location" r =0)
vo~ -I- -tinV = A - . hopen circuit voltage
0. ce h atinceq
soI = .9h H in. short circuit currenteq
B. =p H.inc o inc
V .V 0 + s voltage into loadT-(2.4)
C
L
I = c current into loadS. C.ls2.
s~.1 + ý
c
Vc. = sL source impedance
S. C,
- = Z load impedance
T cI
LhL h j h h
eq eq eq o eq eq eq
%0
III. High Frequency Limitation
Assuming that the sensor is desired to have a time-derivativebehavior then we need to determine some maximum frequency w = 2irf
C C
for which this time-derivative behavior is followed. This is the sensorbandwidth for a time-derivative sensor. Corresponding to the character-
istic time which might be defined in terms of w or might be definedc
directly in terms of a time domain measurement or calculation.
For electric dipole sensors the time derivative behavior is asso-
ciated with the short circuit current characterized by an equivalent area
Aeeq. For magnetic dipole sensors the time derivative behavior is asso-
ciated with the open circuit voltage characterized by an equivalent area
Aheq. Note that these equivalent areas are constant vectors by definition;
they are vector coefficients in the asymptotic forms of the low frequency
response.
In summary then we have the iHeal sensor behavior for time-
derivative operation
I A D. electric dipole sensorideal e at inc
eq(3.1)
ide = at inc magnetic dipole sensoreq
or in frequency domain
"a A~ -• iIid = -sA • D electric dipole sensorieal e inc
eq"(3.2)
ideal= s B c magnetic dipole sensoreq
We are then interested in characteristic frequencies or times for which
V and I begin to deviate from the ideal form above.
1\
Ona possible definition of the bandwidth is
C electric dipole sensorc
w = 2 7'f = 1 = (3 3c c t =(3 )
c Z1 magnetic dipole sensor
where these correspond to frequencies that the magnitude of the response
is 1/05 times the ideal magnitude. This is based on the equivalent cir-
cuit and is a very natural definition for cases that t >> transit times onC
the sensor, i.e. for cases that the sensor is still electrically small at
this characteristic frequency.
1However, as has been discussed previously, maximizing the equiva-
lent area for a given upper frequency limit implies increasing the sensor
size until transit time limits are of the same order as circuit relaxation
tirie limits (CZ or L/Z ). Hence a sensor with maximum bandwidth forc c
a given sensitivity (equivalent area) will not be able to directly use the
definitions in equations 3. 3.
It would be desirable to have a definition of w and/or t which canc c
be directly measured in CW and/or transient experiments. Let us men-
tion a few possible definitions. For CW purposes (or from transformed
time-domain data) one might define w as the first frequency for which thec
response magnitude deviated from its ideal form by some fractional
amount •, i.e.
V(iWc -1 for w -w (3.4)
Videal( i) c
Note that voltage or current can be used interchangeably since they are
related by the constant impedance Z . Since the sensor response is ac
function of the directions of incidence 11 and field directions 12 and 1 TO
12.
and since for a non-electrically-small sensor V(iw) does not in general
have the simple dot-product angular dependence (equations 2.2 and 2.4)
as does V ideal(i), then this limitation may have been imposed in an upperbound sense over all directions of incidence and field directions. Another
approach might be to define a weighted average of the left side of equation
3.4 (averaged over directions of incidence and/or field directions) and
require this weighted average to be less than or equal to E.
In time domain one might excite the sensor by an ideal type of tran-
sient wave, say a step function of near zero rise time. Integrating the
sensor output gives a step-like waveform, the early portion oJ which can
be used to define t . If there is no significant overshoot or other pro-c
nounced oscillatory behavior one might define some kind of rise time such
as the usual 10% to 90% or some other form (0% to 50%, etc. ). If this is
taken as some At then one might define t in any of several ways such asc
t E Atc
tc E max (At) by varying I1, etc.
tc = avg (At) with appropriatc -.-eighting
Having define w and/or t this can be converted to characteristicc c
length I byc
S= ct (3.6)c c
and/orC (3.7)
C W c"* c
This parameter .Q will be used in defining the figure of merit.c
Note that there are many possible detailed ways to define wc, t ,ccand .e . One should be specific in the definition. To distinguish onec
choice from another one might use subscripts, for example 10-90 based
on 10% to 90% rise time, or 10.3 based on a deviation of the r,;sponse
magnitude of 30%, etc.
IV. Figure of Merit
The figure of merit, which might be referred to as a sensitivity-
bandwidth figure of merit, is defined in a manner such that a larger value
of this parameter means a larger bandwidth for a given sensitivity, or
conversely a larger sensitivity for a given bandwidth. The figure of merit
should combine the sensitivity and bandwidth in a manner which gives a
number independent of size of the sensor, i.e. in scaling the sensor
dimensions this number should not change. This indicates that the sensi-
tivity which is an area and the bandwidth will combine like sensitivity
times bandwidth squared, i.e. like A W2 or A t-2eq c eq c
A. Definition of figure of merit
'raking the incident wave as defined in equations 1. 6 consider the
ideal voltage normalized to the incident electric field multiplied by the
normalized bandwidth as the definition of a voltage figure of merit AV*
specifically
V ideal iWc) W c V ideal OW c 1AV-- =- (4.1)
E f( c ) c Eof(i0) c
For this definition the orientation of the field (electric or magnetic depend-
ing on sensor type) is taken parallel to A to maximize the result, andeq
where the ideal voltage is evaluated at s = iW to maximize the result.c
Similarly define a current figure of merit AI with the current normalized
to the incident magnetic field as
fide OW c) .ideal2) c
Ho0f (1wc ) H f(i) co c o
These definitions both apply to both electric and magnetic dipole sensors.
_k
Both A and A are dimensionless figures of merit but they have a
certain deficiency. If one were to take the sensor output into impedance
Z and introduce an ideal 1 to N turn transformer and change the load
impedance to N 2Z on the transformer secondary the voltage would bec
increased by a factor of N. This would increase AV by a factor of N since
the load on the sensor has remained Z and hence the upper bandwidth hasc
remained w . Similarly the current and AI would be decreased by a factor
of N. To make the figure of merit independent of this type of change to
the sensor output define a figure of merit as
A [Av AI]1/2
VidealOWc) I ideal Wc 1
E f(ic) H f(iw) c
0c EfOw cz 1/2 i=(Zc° Iideal( c) 1
Eof(iw) c
From another point of view this figure of merit combines voltage
and current in the form of the square root of power. Power is conserved
on passing through an ideal transformer. This figure of merit is then inthe form of (power)1/2 times bandwidth.
B. Electric dipole sensor
Applying these results to an electric dipole sensor the ideal voltage
and current from section 3 together with the incident wave giveonpsin hogha delta sfomr Thi fiueoIeitihni
z c -S A e 2 Z c cl)AV Zo 0eeq 0o eq(w5
A -A ~ =A A
e e c eeqeq eq
(Z 1/2 (Z 1/2
The high-frequency figure of merit A is then proportional to ze/Z°
for an electric dipole sensor. The equivalent area and characteristic
lm2 which reappear in the same form in the mag-length form a term Aeeqeqc
netic dipole sensor.
C. Magnetic dipole sensor (loop)
Applying equations 4. 1 through 4. 3 to a magnetic dipole sensor
gives
eq eq
z 2 z 2AI =-- I' hel 2 = Ahq(4.5)A, Z h c ZAh Cf(.5
c eq c eq
1/2
/(Z) 0 e A c =2 (Z)1 02-2q eq
The magnetic dipole sensor then has A proportional to 4ZoFZc, the
0
reciprocal of the factor appearing in the case of the electric dipole sen-
sor. It is this square root of an impedance ratio which makes the figures
of merit for the electric and magnetic dipole sensors comparable. Note
that Aeeq and Aheq are not physically the same since they relate differ-
ent fields to different circuit quantities (volts, current).
! !m l ! l ! mm mm mm m~mmm"I~
V. Extension to Sensors on Ground Planes
The previous discussion has centered around electromagnetic sen-
sors in free space spaced away from other objects. Often it is desired to
mount such sensors on conducting ground planes for measurement of the
surface fields, or equivalently of the surface current and charge densities.
For this purpose the ground plane is assumed to be approximately flat, at
least in the vicinity of the sensor.
Consider a sensor with an electromagnetic symmetry plane8 located
in free space as illustrated in figure 5. 1. In such a situation it measures-0. -1
fields in some incident wave Einc, H inc. It is convenient to define mirror
quantities Eincm and tHinCm via a reflection dyad as
n n
r R rm
-~ (5.1)Einc (r mt) = R Einc (rt)
m
H.n ( t) = - R H Wt)Hinc (rm t) R Hinc (,t
m8
This formalism can be extended to all electromagnetic quantities. Here
1 is the unit dyad (identity) and 1 is a unit vector normal to the symmetryn
plane.
Let us assume that the symmetry plane is replaced by a conducting.8
plane. This forces the fields to be antisymmetric so as to enforce zero
tangential E on the plane, i. e.
E. (r,t) -E .(r,t0 - E rincas 2 nc inctm
(5.2)0.1 -. -. (r0t
H. (r, t) = H. (r, t) - H. rlnas ric(e)inc a2 inc
II1
Minc
sensor
, UL electromagnetic+ ++ , symmetry plansor ground plane
sensoror
sensorimage
Hinc,
Figure 5.1. Electromagnetic Field Sensor with Symmetry Planeor Ground Plane
it
On or near the ground plane the fields are E normal to the plane -nd Htn t-
parallel to the plane, i.e.
0. -40 -. 1
1 X E =0n n
(5.3)
Htt 1 =0n9
eIei ce oily antisymmetric field distributions need be considered (includ-
ing the image in principle). A sensor for use on such a ground plane is
the i appropriate only for measuring the antisymmetric quantities, E and
Ht ,there. Equivalently it is used for measuring surface current and
charge densities through
p5 E 1Ps o n n(5.4)
5 n XHt
Note that in the presence of a ground plane one may consider incident and
reflected fields as separate quantities and refer measurements to them.
More generally since ground planes are often small (say the surface of an
aircraft) it is convenient to refer all measurement to p and J , or ES n
and Ht, as the resulting quantities at the measurement location in the
absence of the sensor. This is the convention adopted here.
In taking a particular type of sensor design and cutting it in half to
mount on a ground plane some of the electrical parameters are changed.
If the original output is differential (say 10091) then the halved sensor is
made to dirive half the impedance (say 50 W) neglecting introduction of
transformers. In the process V is halved with I remaining the same.
"The equivalent area is then halved for magnetic dipole sensors but re-
mains the same for electric dipole sensors. This is summarized in
table 5. 1. Note that the directions of the vector sensitivities for ground
plane application are constrained by
n e. eeq eq
(5.5)
n A = 0, 1 * =0eq eq
The upper frequency response o , has remained unchanged in con-C
version from free space to ground plane since the linear dimensions are
not altered except to remove half the sensor. The sensitivity-bandwidth
figure of merit (equations 4.4 and 4. 5) is then altered as indicated in
table 5.2. Note the factor of 1/ 42 reduction in A which applies to both
electric and magnetic dipole sensors. One should be careful when com-
paring sensor designs whether the free space or ground plane parameters
are being used. The conversion between the two is quite simple.
Cl(
C (ground plane) = 2C (free space)
Z (ground plane) = 1Z(free space)c 2 c
CZ (ground plane) = CZ (free space)electric C C
dipole A (ground plane) = A (free space)e esensor eq eq
e (ground plane) 1 e (free space)e 2eq eq
V (ground plane) = 1V (free space)e 2 e
eq eq
1L (ground plane) = 1L (free space)
Z (ground plane) = 1Z (free space)c 2 c
L/Z (ground plane) = L/Z (free space)c cmagneticdipolesensor Ah. (ground plane) = 21Ah (free space)
eq eq
I (ground plane) = I h (free space)
eq eq
V (ground plane) = 'V (free space)h 2 h
eq eq
.o
Table 5. 1. Change in low-frequency sensor parameters in conversion'" from differential free-space snesor to ground plane version
1|A
w (gr d p ) w (e s
w (ground plane) = w (free space)C c
t (ground plane) 1 t (free space)C c
i (ground plhne) = .• (free sparce)C C
A (ground plane) - 1. A (free s;pace)
Table 5. 2. Change in figure-of-merit parameters inconversion to ground plane sensor
ma
VI. Summary
By defining a dimensionless sensitivity-bandwidth figure of merit A
for electric and magnetic sensors (operated in time-derivative manner)
based on power delivered to a constant resistive load at the sensor's max-
imum frequency response the performance of various sensor designs can
be compared on a common basis. Several sensor designs for high band-
width with given sensitivity have beer realized in various specific models
with various sizes (sensitivities) and application (free space, ground plane).10These are listed in the Electromagnetic Pulse Sensor Handbook. An
important example is the basic MGL (multi-gap loop) design for measur-
ing aB/8t. Taking the MGL-1 data of Aheq = 0. Im 2, measured 10% to 90%
risetime of about 3.0 ns as t , and load impedance of Z = 100 Q2, gives a
figure of merit (free space) of A10_90 = 0.24. Another example is the
basic HSD (hollow spherical dipole) design for measuring aD/Ot. Taking2
the HSD-2 data of Aeeq = 0. 1 m , measured 10% to 90% rise time of about2.7 ns as t , and load impedance of Z = 100 1, gives a figure of merit
c c(free space) of A 10-9) = 0.079. A new aD/8t design is the ACD (asymp-4
totic conical dipole) sensor which has an increased figure of merit,
approaching that of the MGL design.
Having defined the sensitivity-bandwidth figure of merit A for elec-
tromagnetic sensors one can ask some fundamental questions about optimal
sensor design. For example, what is the best way to define I- (from wC c
or t ). This may require some detailed understanding of the high-frequencyc
behavior of transit -tinne -limited time-derivative electromagnetic field sen-
sors. For a given definition of f what is the theoretical maximum A?c
This would give some idea of how close existing designs approach the
optimum performanc( and indicate for future designs when the optimum
performance wa3 beittg approached. For this purpose one might consider
an idealized spherical sensor as a resistive spherical shell and assume all
the power deposited in the shell associated with the lowest E and H modes
were available to drive Z of electric and magnetic dipole sensors resper-Ctively. Such calculations might even suggest sensor desiuns witih largec-
References
1. C. E. Baum, Maximizing Frequency Response of a B Loop, Sensorand Simulation Note 8, December 1964.
2. C. E. Baum, Parameters for Some Electrically-Small Electromag-netic Sensors, Sensor and Simulation Note 38, March 1967.
3. C. E. Baum, The Multi-Gap Cylindrical Loop in Non-ConductingMedia, Sensor and Simulation Note 41, May 1967.
4. C. E. Baum, An Equivalent-Charge Method for Defining Geometriesof Dipole Antennas, Sensor and Simulation Note 72, January 1969.
5. C. E. Baum, Parameters for Electrircally-Small Loops and DipolesExpressed in Terms of Current and Charge Distributions, Sensorand Simulation Note 74, January 1969.
6. C. E. Baum, The Single-Gap Hollow Spherical Dipole in Non-Conducting Media, Sensor and Simuiation Note 91, July 1969.
7. C. E. Baum, Some Characteristics of Electric and Magnetic DipoleAntennas for Radiating Transient Pulses, Sensor and SimulationNote 125, January 1971.
8. C. E. Baum, Interaction of Electromagnetic Fields with an ObjectWhich Has an Electromagnetic Symmetry Plane, Interaction Note 63,March 1971.
9. C. E. Baum and B. K. Singaraju, Generalization of Babinet'sPrinciple in Terms of the Combined Field to Include ImpedanceLoaded Aperture Antennas and Scatterers, Interaction Note 217,September 1974.
10. C. E. Baum, ed., Electromagnetic Pulse Sensor Handbook, EMXPMeasurement 1-1, June 1971 (original issue).